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Gaurav Seth 5 years, 4 months ago
Show that n2 - 1 is divisible by 8, if n is an odd positive integer.
Any odd positive integer n can be written in form of 4q + 1 or 4q + 3.
If n = 4q + 1, when n2 - 1 = (4q + 1)2 - 1 = 16q2 + 8q + 1 - 1 = 8q(2q + 1) which is divisible by 8.
If n = 4q + 3, when n2 - 1 = (4q + 3)2 - 1 = 16q2 + 24q + 9 - 1 = 8(2q2 + 3q + 1) which is divisible by 8.
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Gaurav Seth 5 years, 4 months ago
ome of the nationalist symbols of the countries other than European countries are as under :

These nationalist symbols are very different from the symbols of European countries in the manner that they mainifest nationalist sentiments of their respective countries.
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The dust of snow is the symbol of natural joy and energy. The dust of snow that the crow shakes off a hemlock tree means passing through the sad and depressing moments the pdet is entering into the time full of joy and optimism.
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Gaurav Seth 5 years, 4 months ago
The eighteenth century witnessed the emergence of social groups, termed the middle class, who earned their wealth through an expanding overseas trade and from the manufacture of goods such as woollen and silk textiles that were either exported or bought by the richer members of society. In addition to merchants and manufacturers, the educated in the third estate included professions such as lawyers or administrative officials. They believed that no group in society should be privileged by birth. Rather, a person’s social position must depend on his merit. These ideas envisaging a society based on freedom and equal laws and opportunities for all, paved way for the emergence of the middle class.
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Gaurav Seth 5 years, 4 months ago
Given that the zeroes of the following polynomial are a-b, a and a+b :
We are to find the values of a and b.
We know that if p, q and r are the zeroes of a polynomial then
So, for polynomial (i), we get
and
Thus, the required value of a is 1 and that of b is ±√2.
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Yogita Ingle 5 years, 4 months ago
A chemical equation can give more informations in the following ways:
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